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_:Nf75fd99e6a1f45a6b3c08add264193ee "10.1007/pl00004638" .
_:N1ebbc537c86d44c2befff5f7f2aab767 .
_:N26a0c87724da48178cb9aa88c7c6ca07 "Springer Nature - SN SciGraph project" .
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_:N1ebbc537c86d44c2befff5f7f2aab767 .
"1998-08-01" .
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_:Nf75fd99e6a1f45a6b3c08add264193ee .
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_:Na8bbc7ee665a470c858e59586fe523df .
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"In this paper we introduce the notion of a combinatorial dynamical system on any CW complex. Earlier in [Fo3] and [Fo4], we presented the idea of a combinatorial vector field (see also [Fo1] for the one-dimensional case), and studied the corresponding Morse Theory. Equivalently, we studied the homological properties of gradient vector fields (these terms were defined precisely in [Fo3], see also Sect. 2 of this paper). In this paper we broaden our investigation and consider general combinatorial vector fields. We first study the homological properties of such vector fields, generalizing the Morse Inequalities of [Fo3]. We then introduce various zeta functions which keep track of the closed orbits of the corresponding flow, and prove that these zeta functions, initially defined only on a half plane, can be analytically continued to meromorphic functions on the entire complex plane. Lastly, we review the notion of Reidemeister Torsion of a CW complex (introduced in [Re], [Fr]) and show that the torsion is equal to the value at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $z=0$\\end{document} of one of the zeta functions introduced earlier. Much of this paper can be viewed as a combinatorial analogue of the work on smooth dynamical systems presented in [P-P], [Fra], [Fri1, 2] and elsewhere." .
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"Mathematical Sciences" .
_:N26a0c87724da48178cb9aa88c7c6ca07 .
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"Combinatorial vector fields and dynamical systems" .
_:Nf75fd99e6a1f45a6b3c08add264193ee .
"Forman" .
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"1998-08" .
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"articles" .
_:Nf75fd99e6a1f45a6b3c08add264193ee "doi" .
_:N12e142bf6da34a0fbc3d4880eead5ac2 .
"1432-1823" .
"Mathematische Zeitschrift" .
_:Na8bbc7ee665a470c858e59586fe523df "228" .
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_:N12e142bf6da34a0fbc3d4880eead5ac2 "pub.1027904863" .
_:N26a0c87724da48178cb9aa88c7c6ca07 .
"Pure Mathematics" .
"http://link.springer.com/10.1007%2FPL00004638" .
"Department of Mathematics, Rice University, Houston, TX 77251, USA (e-mail: forman@math.rice.edu), US" .
"Rice University" .
"2019-04-10T23:28" .
_:Nf6b6cee552b24e9ea082c8f6a29f6b85 .
"629-681" .
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